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@article{Liebeck:2021,
author = {Liebeck, M and Shalev, A and Tiep, PH},
journal = {Transactions of the American Mathematical Society},
pages = {5651--5676},
title = {McKay graphs for alternating and classical groups},
url = {http://hdl.handle.net/10044/1/86656},
volume = {374},
year = {2021}
}

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TY  - JOUR
AB  - Let G be  a  finite  group,  andαa  nontrivial  character  of G.   The  McKay graph M (G,α) has the irreducible characters of Gas vertices, with an edge fromχ1toχ2ifχ2is a constituent ofαχ1. We study the diameters of McKay graphs for finite simple groups G.  For alternating groups G=An, we prove a conjecture made in [20]:  there is an absolute constant C such that diam M (G,α)≤ C log | G| log α (1)for all nontrivial irreducible characters α of G.  Also for classical groups of symplectic or orthogonal type of rank r, we establish a linear upper bound Cr on the diameters of all nontrivial McKay graphs. Finally,  we  provide  some  sufficient  conditions  for  a  productχ1χ2···χlof  irreducible characters of some finite simple groups G to contain all irreducible characters of G as constituents.
AU  - Liebeck,M
AU  - Shalev,A
AU  - Tiep,PH
EP  - 5676
PY  - 2021///
SN  - 0002-9947
SP  - 5651
TI  - McKay graphs for alternating and classical groups
T2  - Transactions of the American Mathematical Society
UR  - http://hdl.handle.net/10044/1/86656
VL  - 374
ER  -

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